Aircraft: MD-11
Phase of flight: Cruise; Climb; Descent; Initial Climb
Anomaly: Aircraft Equipment Problem Critical

I operated as the Captain and Pilot Monitoring on the flight. Prior to leaving the hotel; we were contacted by Crew Scheduling. Crew Scheduling notified us about the flight being delayed from its original scheduled departure time due to maintenance. The anticipated delay was six hours. We arrived at the aircraft and started our normal preflight duties. Several items were deferred: MEL 28-22-1-2-1 #2 left aft main tank pumps (tank 2 aft auto mode) and MEL 31-65-1 multifunction control display unit (DCU) #3. During preflight; we received a Level 1 'TR 3 Fail' alert and a subsequent FMC #2 fail. I entered the items into the logbook in accordance with FOM flight crew handling of aircraft discrepancies and notified Local Maintenance. Three Maintenance personnel arrived at the aircraft and we left the flight deck in order for Maintenance to work on the problems. Maintenance cleared the Level 1 'TR 3 Fail' and deferred FMC #2. I requested and received amended release #1 adding MEL 34-63-1; #2 FMC INOP - No RNP 4 operations. The crew reviewed MEL 34-63-1 operations procedures and operational limitations. Furthermore; we discussed the ramifications of one FMC operation and two (of three) MCDU's. The flight blocked out and shortly after departure; we received a Level 1 'TR 3 Fail' alert. DU 4; 5; 6 and MCDU #2 lost brief power approximately every seven to 10 minutes causing all three display units and MCDU #2 to blink off and then on. This event required the First Officer to reselect FMC #1 on MCDU #2. We cross checked all displays and no errors were noted between the First Officer's displays and my side. We discussed the problem and determined the First Officer would continue to be the Pilot Flying unless we had a longer display failure. I continued to monitor the situation as Pilot Monitoring and discussed that we would contact Maintenance Control at the top of the climb. We selected and utilized autopilot 1 (AP1) for climb out and cruise. Upon leveling at FL310; we continued to observe a Level 1 'TR 3 Fail' alert. DU 4; 5; 6 and MCDU #2 lost power with increased frequency. TR 3 showed a load of 0.03-0.04. We also; received Level 1 'FIRE DET 2 FAULT' alert. I asked the First Officer to continue to fly and monitor ATC along with the IRO. I contacted our Dispatcher; Maintenance; and requested to speak with a Systems Maintenance Expert via SAT phone. Up until this point; we felt there were no flight safety concerns to operating the aircraft on the intended flight. We did not feel that a complete failure of MCDU #2 was imminent. Also; we believed the power interruptions to DU 4; 5; 6; and MCDU#2 were due to the opening and closing of the TR #3 relay. After discussing the situation with Dispatch; the Maintenance expert; and the crew; we elected to perform an Air Turn Back to Dispatch requested departure airport. I requested and received amended release #2 to change our destination to the Dispatch requested destination. We were given a nearby airport as the alternate. Later; we received an amended release #3 changing destination alternate due to changing weather conditions at the destination. In consultation with Dispatch; the crew did not feel the need to declare an emergency. We coordinated with ATC and dumped approximately 15;000 pounds of fuel to reduce to below max landing weight. Fuel dump was completed. DU 4; 5; 6 and MCDU #2 continued to blink off and on more frequently. During the descent; DU 4 began to intermittently display a RED X during the power cycle. We discussed the increased frequency of cycle times; and landing weather and I decided it would be best for me to assume the Pilot Flying duties. A positive transfer of aircraft control was performed and the First Officer assumed the Pilot Monitoring duties for the remainder of the flight. During descent; DU 4; 5; 6 and MCDU #2 continued to briefly lose power (blink off/on) approximately every 30 seconds. On final approach; MCDU #2 failed. A normal landing was made. Again; in consultation with Dispatch; the crew did not feel the need to declare an emergency. The crew did not feel the safety of the flight was ever compromised nor did we need to deviate from an ATC clearance to safely complete the Air Turn Back. [This Report contains no additional information]. An MD-11 departed with several MEL's and shortly after takeoff a Level 1 TR 3 FAIL alerted which resulted in DU's 4; 5; 6 and MCDU #2 power loss. The flight returned to land at an alternate airport without declaring an emergency.